Broadcasting of entanglement via orthogonal and non-orthogonal state-dependent cloners

Abstract

In this work, we extensively study the problem of broadcasting of entanglement as state-dependent versus state-independent cloners. We start by re-conceptualizing the idea of state-dependent quantum cloning machine (SD-QCM), and in that process, we introduce different types of SD-QCMs, namely orthogonal and non-orthogonal cloners. We derive the conditions for which the fidelity of these cloners will become independent of the input state. We note that such a construction allows us to maximize the cloning fidelity at the cost of having partial information of the input state. In the discussion on broadcasting of entanglement, we start with a general two-qubit state as our resource and later we consider a specific example of Bell diagonal state. We apply both state-dependent and state-independent cloners (orthogonal and non-orthogonal), locally and non-locally, on input resource state and obtain a range for broadcasting of entanglement in terms of the input state parameters. Our results highlight several instances where the state-dependent cloners outperform their state-independent counterparts in broadcasting entanglement. Our study provides a comparative perspective on the broadcasting of entanglement via cloning in two-qubit scenario, when we have some knowledge of the resource ensemble versus a situation when we have no such information.